The Generating Function for Laguerre Polynomials

We use the recursion relation for Laguerre polynomials ( • Recursion Relation for... ) to find a closed form expression for the generating function of the Laguerre polynomials. Generating functions play an essential role in discovering values of these polynomials at certain points and relationships among the derivatives of these functions. The generating function, and its generalizations, are very useful in the study of the Schrodinger equation for the hydrogen atom.
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